Question #54391

Assume that there are four firms supplying a homogenous product. They have identical cost functions given by C (Q) = 40 Q. If the demand curve for the industry is given by µ = 100 – Q, find the equilibrium industry output if the producers are Cournot competitors. What would be the resultant market price? What are the profits of each firm?

Expert's answer

If the firms have identical cost functions given by C (Q) = 40 Q, so every firm produce the quantity, for which MR = MC.

MC = C' = 40

MR = TR' = (P*Q)' = ((100 - Q)*Q)' = 100 - 2Q

So, 100 - 2Q = 40,

Q = 30

So, the equilibrium industry output if the producers are Cournot competitors is 30*4 = 120 units.

The market price is P = 100 - 30 = $70.

Total profits of each firm are: TP = TR - TC = P*Q - TC = 70*30 - 40*30 = $900.

MC = C' = 40

MR = TR' = (P*Q)' = ((100 - Q)*Q)' = 100 - 2Q

So, 100 - 2Q = 40,

Q = 30

So, the equilibrium industry output if the producers are Cournot competitors is 30*4 = 120 units.

The market price is P = 100 - 30 = $70.

Total profits of each firm are: TP = TR - TC = P*Q - TC = 70*30 - 40*30 = $900.

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